Context. Tidal tails of star clusters are commonly understood to be populated symmetrically. Recently, the analysis of Gaia data revealed large asymmetries between the leading and trailing tidal tail arms of the four open star clusters Hyades, Praesepe, Coma Berenices and NGC 752. Aims. As the evaporation of stars from star clusters into the tidal tails is a stochastic process, the degree of stochastic asymmetry is quantified in this work. Methods. For each star cluster 1000 configurations of test particles are integrated in the combined potential of a Plummer sphere and the Galactic tidal field over the life time of the particular star cluster. For each of the four star clusters the distribution function of the stochastic asymmetry is determined and compared with the observed asymmetry. Results. The probabilities for a stochastic origin of the observed asymmetry of the four star clusters are: Praesepe ≈1.7 σ, Coma Berenices ≈2.4 σ, Hyades ≈6.7 σ, NGC 752 ≈1.6 σ. Conclusions. In the case of Praesepe, Coma Berenices and NGC 752 the observed asymmetry can be interpreted as a stochastic evaporation event. However, for the formation of the asymmetric tidal tails of the Hyades additional dynamical processes beyond a pure statistical evaporation effect are required.